{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical Clustering\n",
    "\n",
    "Hierarchical clustering involves creating clusters that have a predetermined ordering from top to bottom. For example, all files and folders on the hard disk are organized in a hierarchy. There are two types of hierarchical clustering, Divisive and Agglomerative.\n",
    "\n",
    "**Divisive method**\n",
    "\n",
    "In this method we assign all of the observations to a single cluster and then partition the cluster to two least similar clusters. Finally, we proceed recursively on each cluster until there is one cluster for each observation.\n",
    "\n",
    "**Agglomerative method**\n",
    "\t\t\n",
    "In this method we assign each observation to its own cluster. Then, compute the similarity (e.g., distance) between each of the clusters and join the two most similar clusters. Finally, repeat steps 2 and 3 until there is only a single cluster left.\n",
    "\n",
    "## Linkage or distance matrix\n",
    "\n",
    "Before any clustering is performed, it is required to determine the proximity matrix containing the distance between each point using a distance function. Then, the matrix is updated to display the distance between each cluster. The following three methods differ in how the distance between each cluster is measured.\n",
    "\n",
    "**Single Linkage** \t\t\n",
    "In single linkage hierarchical clustering, the distance between two clusters is defined as the shortest distance between two points in each cluster. For example, the distance between clusters “r” and “s” to the left is equal to the length of the arrow between their two closest points.\n",
    "<img src=http://www.saedsayad.com/images/Clustering_single.png>\n",
    "\n",
    "**Complete Linkage**\t\t\n",
    "In complete linkage hierarchical clustering, the distance between two clusters is defined as the longest distance between two points in each cluster. For example, the distance between clusters “r” and “s” to the left is equal to the length of the arrow between their two furthest points.\n",
    "<img src=http://www.saedsayad.com/images/Clustering_complete.png>\n",
    "\n",
    "**Average Linkage**\t\n",
    "In average linkage hierarchical clustering, the distance between two clusters is defined as the average distance between each point in one cluster to every point in the other cluster. For example, the distance between clusters “r” and “s” to the left is equal to the average length each arrow between connecting the points of one cluster to the other.\n",
    "<img src=http://www.saedsayad.com/images/Clustering_average.png>\n",
    "\n",
    "## Dendograms\n",
    "\n",
    "[Dendograms](https://en.wikipedia.org/wiki/Dendrogram) are tree diagrams frequently used to illustrate the arrangement of the clusters produced by hierarchical clustering. The clades are arranged according to how similar (or dissimilar) they are. Clades that are close to the same height are similar to each other; clades with different heights are dissimilar — the greater the difference in height, the more dissimilarity. \n",
    "\n",
    "An example involving the famous Iris data set is shown below.\n",
    "\n",
    "<img src=https://upload.wikimedia.org/wikipedia/commons/1/12/Iris_dendrogram.png height='400px' width = '400px'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering with a shopping trend data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read in the data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age</th>\n",
       "      <th>Annual Income (k$)</th>\n",
       "      <th>Spending Score (1-100)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>15</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>21</td>\n",
       "      <td>15</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Female</td>\n",
       "      <td>20</td>\n",
       "      <td>16</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Female</td>\n",
       "      <td>23</td>\n",
       "      <td>16</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>Female</td>\n",
       "      <td>31</td>\n",
       "      <td>17</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>Female</td>\n",
       "      <td>22</td>\n",
       "      <td>17</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>Female</td>\n",
       "      <td>35</td>\n",
       "      <td>18</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>Female</td>\n",
       "      <td>23</td>\n",
       "      <td>18</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>Male</td>\n",
       "      <td>64</td>\n",
       "      <td>19</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>Female</td>\n",
       "      <td>30</td>\n",
       "      <td>19</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID  Gender  Age  Annual Income (k$)  Spending Score (1-100)\n",
       "0           1    Male   19                  15                      39\n",
       "1           2    Male   21                  15                      81\n",
       "2           3  Female   20                  16                       6\n",
       "3           4  Female   23                  16                      77\n",
       "4           5  Female   31                  17                      40\n",
       "5           6  Female   22                  17                      76\n",
       "6           7  Female   35                  18                       6\n",
       "7           8  Female   23                  18                      94\n",
       "8           9    Male   64                  19                       3\n",
       "9          10  Female   30                  19                      72"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('Datasets/Mall_Customers.csv')\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Age</th>\n",
       "      <th>Annual Income (k$)</th>\n",
       "      <th>Spending Score (1-100)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>100.500000</td>\n",
       "      <td>38.850000</td>\n",
       "      <td>60.560000</td>\n",
       "      <td>50.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>57.879185</td>\n",
       "      <td>13.969007</td>\n",
       "      <td>26.264721</td>\n",
       "      <td>25.823522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>50.750000</td>\n",
       "      <td>28.750000</td>\n",
       "      <td>41.500000</td>\n",
       "      <td>34.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>100.500000</td>\n",
       "      <td>36.000000</td>\n",
       "      <td>61.500000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>150.250000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>78.000000</td>\n",
       "      <td>73.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>200.000000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>137.000000</td>\n",
       "      <td>99.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       CustomerID         Age  Annual Income (k$)  Spending Score (1-100)\n",
       "count  200.000000  200.000000          200.000000              200.000000\n",
       "mean   100.500000   38.850000           60.560000               50.200000\n",
       "std     57.879185   13.969007           26.264721               25.823522\n",
       "min      1.000000   18.000000           15.000000                1.000000\n",
       "25%     50.750000   28.750000           41.500000               34.750000\n",
       "50%    100.500000   36.000000           61.500000               50.000000\n",
       "75%    150.250000   49.000000           78.000000               73.000000\n",
       "max    200.000000   70.000000          137.000000               99.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gIuAU4MYkW9oNbgFuWsy6JEnSPoOcZf2I9siYJA8Gngx8EfgwcFo722nAh1YqSEmS1rsN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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22450c6eb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Annual income distribution\",fontsize=16)\n",
    "plt.xlabel (\"Annual income (k$)\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.hist(df['Annual Income (k$)'],color='orange',edgecolor='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BwJnNbXXmlcAlLbfty6l5P/CdzLwf8CBKn9qXkxQRBwD/D+jNzEMpg2yfiX3Z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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22451146da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Spending Score distribution\",fontsize=16)\n",
    "plt.xlabel (\"Spending Score (1-100)\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.hist(df['Spending Score (1-100)'],color='green',edgecolor='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### So, is there a definitive correlation between annual income and spending score? - *Apparently not*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/+MU+KkHyxHLh1z1/7Fj+4fWSa7czLj+fqXY7e7ZuxROiX9CeKDX9ie7wMwDt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\ndgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2244f936b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Annual Income and Spending Score correlation\",fontsize=18)\n",
    "plt.xlabel (\"Annual Income (k$)\",fontsize=14)\n",
    "plt.ylabel (\"Spending Score (1-100)\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.scatter(df['Annual Income (k$)'],df['Spending Score (1-100)'],color='red',edgecolor='k',alpha=0.6, s=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How about correlation between age and spending score? - *Apparently not*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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be82aR6moWMmaNY9y443XRRWtjR8/nhUrFuPxfJP6+pV0dFShlIeOjirq658G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\nBl9RFEVR8gBt8BVFURQlD/j/Ri0D6gvBpKkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2244f930320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Age and Spending Score correlation\",fontsize=18)\n",
    "plt.xlabel (\"Age\",fontsize=14)\n",
    "plt.ylabel (\"Spending Score (1-100)\",fontsize=14)\n",
    "plt.grid(True)\n",
    "plt.scatter(df['Age'],df['Spending Score (1-100)'],color='blue',edgecolor='k',alpha=0.6, s=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Strategy\n",
    "** Therefore, we will explore cluserting the customers based on their annual income and spending score to see if there are distinguisbale clusters which the mall can target **\n",
    "\n",
    "We could use k-means but we don't have any idea about the number of hidden clusters. We will see that hierarchial clustering with dendograms will give us a good insight on the optimal number of clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dendograms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.iloc[:,[3,4]].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### _Ward_ distance matrix\n",
    "We will use 'Ward' distance matrix for this dendogram.\n",
    "$$d(u,v) = \\sqrt{\\frac{|v|+|s|}{T}d(v,s)^2+ \\frac{|v|+|t|}{T}d(v,t)^2- \\frac{|v|}{T}d(s,t)^2}$$\n",
    "\n",
    "where **$u$** is the newly joined cluster consisting of clusters **$s$** and **$t$**, **$v$** is an unused cluster in the forest, **$T=|v|+|s|+|t|$**, and **$|*|$** is the cardinality of its argument. This is also known as the incremental algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wSP4AAAAAoAZI/gAAAACgBkj+AAAAAKAGSP4AAAAAoAZI/gAAAACgBkj+AAAA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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x224589ed8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.cluster.hierarchy as sch\n",
    "\n",
    "plt.figure(figsize=(15,6))\n",
    "plt.title('Dendrogram')\n",
    "plt.xlabel('Customers')\n",
    "plt.ylabel('Euclidean distances')\n",
    "#plt.grid(True)\n",
    "dendrogram = sch.dendrogram(sch.linkage(X, method = 'ward'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimal number of clusters\n",
    "\n",
    "Often, the optimal number of clusters can be found from a Dendogram is a simple manner.\n",
    "* Look for the longest stretch of vertical line which is not crossed by any ***extended*** horizontal lines (here *extended* means horizontal lines i.e. the cluster dividers are extended infinitely to both directions).\n",
    "* Now take any point on that stretch of line and draw an imaginary horizontal line.\n",
    "* Count how many vertical lines this imaginary lines crossed.\n",
    "* That is likely to be the optimal number of clusters.\n",
    "\n",
    "**The idea is shown in the following figure. Here the optimal number of clusters could be 5.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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55ptv1uGHHx7vS41q5syZWrVqlc4991yNGDGi2P5DDz20yHanTp2iznD8y1/+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\nx3EmAP8PLy5v1+VkW5wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22451012240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,6))\n",
    "plt.title('Dendrogram')\n",
    "plt.xlabel('Customers')\n",
    "plt.ylabel('Euclidean distances')\n",
    "plt.hlines(y=190,xmin=0,xmax=2000,lw=3,linestyles='--')\n",
    "plt.text(x=900,y=220,s='Horizontal line crossing 5 vertical lines',fontsize=20)\n",
    "#plt.grid(True)\n",
    "dendrogram = sch.dendrogram(sch.linkage(X, method = 'ward'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hierarchical Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "hc = AgglomerativeClustering(n_clusters = 5, affinity = 'euclidean', linkage = 'ward')\n",
    "y_hc = hc.fit_predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the clusters and label customer types\n",
    "* _Careful_ - high income but low spenders\n",
    "* _Standard_ - middle income and middle spenders\n",
    "* **_Target group_ - middle-to-high income and high spenders (should be targeted by the mall)**\n",
    "* _Careless_ - low income but high spenders (should be avoided because of possible credit risk)\n",
    "* _Sensible_ - low income and low spenders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WD9gY6cXOuTuBOwFGjhzpysvLU9PraGqqvGi66ge8G/gCXb0yh6FXdewq75vT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\ni4jkos5x628u8xv3VF+b3H5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g1o50xDn3DyBS0fkJHdmuSDo1l6Lccot3BbS21osZPOMM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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x224585970b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,7))\n",
    "plt.scatter(X[y_hc == 0, 0], X[y_hc == 0, 1], s = 100, c = 'red', label = 'Careful')\n",
    "plt.scatter(X[y_hc == 1, 0], X[y_hc == 1, 1], s = 100, c = 'blue', label = 'Standard')\n",
    "plt.scatter(X[y_hc == 2, 0], X[y_hc == 2, 1], s = 100, c = 'green', label = 'Target group')\n",
    "plt.scatter(X[y_hc == 3, 0], X[y_hc == 3, 1], s = 100, c = 'orange', label = 'Careless')\n",
    "plt.scatter(X[y_hc == 4, 0], X[y_hc == 4, 1], s = 100, c = 'magenta', label = 'Sensible')\n",
    "plt.title('Clustering of customers',fontsize=20)\n",
    "plt.xlabel('Annual Income (k$)',fontsize=16)\n",
    "plt.ylabel('Spending Score (1-100)',fontsize=16)\n",
    "plt.legend(fontsize=16)\n",
    "plt.grid(True)\n",
    "plt.axhspan(ymin=60,ymax=100,xmin=0.4,xmax=0.96,alpha=0.3,color='yellow')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Verifying the optimal number of clusters by k-means algorithm\n",
    "\n",
    "Given a set of observations $(x_1, x_2, …, x_n)$, where each observation is a d-dimensional real vector, [**k-means clustering**](https://en.wikipedia.org/wiki/K-means_clustering) aims to partition the *$n$* observations into *$k$* (≤ *$n$*) sets $S = {S_1, S_2, …, S_k}$ so as to minimize the within-cluster sum of squares (WCSS) (i.e. variance). Formally, the objective is to find:\n",
    "\n",
    "$${\\displaystyle {\\underset {\\mathbf {S} }{\\operatorname {arg\\,min} }}\\sum _{i=1}^{k}\\sum _{\\mathbf {x} \\in S_{i}}\\left\\|\\mathbf {x} -{\\boldsymbol {\\mu }}_{i}\\right\\|^{2}={\\underset {\\mathbf {S} }{\\operatorname {arg\\,min} }}\\sum _{i=1}^{k}|S_{i}|\\operatorname {Var} S_{i}}$$\n",
    "\n",
    "where $\\mu_i$ is the mean of points in $S_i$\n",
    "\n",
    "We run k-means++ model (k-means with carefully initialized centroids) iterating over number of clusters (1 to 15) and plot the ***within-cluster-sum-of-squares (WCSS) matric*** to determine the optimum number of cluster by elbow method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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77z306tWrUoOl4jJy5fANz8CekDRcjcnGiEYG2N67jqbDIiIiIqqRSkyec3Jy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RVQKRERkXmZHJ7Hjx+P8+fPY+/evdi1axf8/PzQsmVLhIWFISwsDG5ubuVZJxGVM4lIwPwQOXwd\nJPgkKt1gS+///p6N+Cw1/vtayVt6DxkypGIKJSIiMiOT16OaMWMGDh48iDt37mDXrl3o2bMn4uLi\nMHbsWNSvXx9BQUEYN25cmRY3Z84cyOVyg4+6devqj2u1WsyZMwf16tWDu7s7unXrhlu3bhlcIzc3\nF5MnT4aPjw+qV6+Od955B3/99ZfBOWlpaRg+fDi8vLzg5eWF4cOHIy0tzeCcu3fvol+/fqhevTp8\nfHwwZcoU5OXllen7JaoM3q9vi22vO8NeatjLfOJ+LjrtS8SfGaoSnklERPTyK/VirhYWFmjdujWm\nTJmC+fPnY+bMmahTpw5u376NTZs2lXmBvr6+iImJ0X+cO3dOf2zJkiVYsWIF5s2bh2PHjkGhUKBX\nr17IzCxcv3bq1KnYs2cP1q1bh/379yMzMxP9+vWDWl24PtewYcNw/fp17NixAzt27MD169cxYsQI\n/XG1Wo1+/fohKysL+/fvx7p16/DTTz9h2rRpZf5+iSqDDh6WONRNAS9bw+Xqfk9XocPeRJz7J7eE\nZxIREb3cSrXaxo0bN3Du3Dn9KhtJSUkAAA8PD/Tt2xdhYWFlX6BE8tQhIVqtFqtWrcL48eP1a0uv\nWrUKvr6+2LFjB4YOHYr09HRs3LgRK1asQLt27QAAa9asQaNGjXDixAl06NABMTExOHLkCA4ePIgW\nLVoA0G0I07VrV8TGxsLX1xfHjh3DrVu3cOPGDXh6egIAPv/8c4wbNw6fffYZ7O3ty/x9E5lbfUcp\njr6pwICjKYhOLPwrS0quBj0PJWFpS0e8U8fajBUSERFVPJPDc82aNZGZmQmtVgs/Pz9069ZNv8tg\nQaAsD/Hx8ahXrx5kMhmaNWuG6dOnw9vbGwkJCXjw4AHat2+vP9fKygphYWGIiorC0KFDcfXqVSiV\nSoNzPD094efnh6ioKHTo0AHR0dGwtbVFcHCw/pyQkBDY2NggKioKvr6+iI6Ohp+fn8H77NChA3Jz\nc3H16lW0adOmxPpjY2PL+I5UbbwfL66i72GEL/AlZDiUWPjjIk8DjDydiuj4hxjhpYSReYSVFr8X\nXxzvYdngfXxxvIcvjvewkK+vr9HjJofngQMHIjQ0FKGhoXBycnrhwkzRrFkzrFy5Er6+vkhKSsKC\nBQvQqVMnXLhwAQ8ePAAAKBQKg+coFAr8/fffAICHDx9CLBbD2dm52DkPHz7Un+Ps7GywDJcgCHBx\ncTE458nXcXZ2hlgs1p9Tkmf9B3iVFPTk0/Mz1z3cWleLeVczMfeq4Zbe392VIkVsj1WtHRHzyzWD\nYwEBARVZYqnwe/HF8R6WDd7HF8d7+OJ4D0vH5PA8a9as8qzjqV5//XWDr5s3b44mTZrg+++/R/Pm\nzSu8HqJXlSAI+CTQHnUcJBjzxJbeu+If426WCpdGvwVkJunbn5x0S0RE9DIoccJgRkbGc1/0RZ5r\njI2NDerVq4fbt2/rx0EnJiYanJOYmAhXV1cAgKurK9RqNZKTk42ek5ycDK22cF0urVaLpKQkg3Oe\nfJ3k5GSo1Wr9OUSvgrd8rPFTZxe4WBr+6LiUpATGbwGq1S3hmURERC+HEsOzv78/vvjiCyQkJJh8\nsTt37mDmzJnw9/cvk+KelJOTg9jYWLi5uaFmzZpwc3PD8ePHDY6fP39eP345ICAAUqnU4Jy//voL\nMTEx+nNatGiBrKwsREdH68+Jjo7Go0ePDM6JiYkxWOLu+PHjsLCwqNR/miYqD8FuFjj6pgL15U/8\n4cqpOjBuE9Cg5DkAREREVV2JwzaWLVuGOXPmYPHixQgMDES7du0QEBAAb29vyOVyaLVapKWlISEh\nAVevXsXx48dx5coV1K1bF8uXLy+T4v7v//4PXbp0gaenp37Mc3Z2Nt59910IgoBRo0YhIiICvr6+\nqFOnDhYuXAgbGxu89dZbAAAHBwcMHDgQM2bMgEKhgKOjI6ZNm4aGDRvitddeAwD4+fmhY8eOmDBh\ngn6HtAkTJqBz58768T/t27dH/fr1MXLkSMyaNQupqamYPn06Bg0axJU26JVU0063pfe/T6TgaJEt\nvWFpA7y3HIi7iM9/TkegiwxNXaTwsBFze28iInoplBiew8PD0b17dxw4cACbN2/GsmXLkJeXV+wX\noFarhaWlJTp06IDJkyejc+fOZfZL8v79+xg2bBiSk5Ph4uKCZs2a4fDhw/Dy8gIAfPjhh3j8+DEm\nT56MtLQ0BAUFYefOnbCzs9NfY86cORCLxRg6dChycnLQpk0brF69GmJx4fq1a9euxZQpU9CnTx8A\nQNeuXTF//nz9cbFYjB9++AGTJk1Cly5dYGlpib59++LLL78sk/dJVBU5yET4oaMzpkal49vfCrf0\nhkgM1A3B1zey9E2uViI0zQ/SBZ+dLMVPuSoREVHlJqSlpWmffRr0y7L9/vvvSE1NBQA4OTnBz89P\nPzyCyBjO5n1xlfUerrmZhY/Pp+iCs4m87cRo6iJDoIsUQS4yNHGWwkZa6n2bnktlvY9VCe9h2eB9\nfHG8hy+O97B0TF5tw8LCAsHBwQbrIRMRAcCIBrb4+N/vAH2mAS5eJj0nPlON+MzH2PnnYwCASADq\nOUgQqJAhKL93uoGjFDIxh3sQEVHlUaodBomISvTbGeCrrrrw7NUIo+aswOUkJa4nK/FY/ew/cGm0\nwM00FW6mqbA5NhsAYCEG/B2laKqQ6Yd7+DpIIOL4aSIiMhOGZyIqW0l3gKQ7mBO8GQCg0mhxK02F\nK0l5uJSYh8tJStxMVcKEPI1ctW4ZvEtJSgC6cdV2UgEBzvljpxW6QO3JCYlERFRBGJ6JqFxJRAIa\nOUnRyEmKQXVtAADZKg1uJCtxOUmJK0m6QB2XoTLpeplKLU7/k4fT/+Tp2xSWIjR1kSLQRYag/EDt\nzAmJRERUDhieiajCWUtECHazQLCbhb4tLVeDq8m6IH05MQ+Xk/JwP1tj0vUSczQ4dC8Xh+4VLpvn\nZaubkBjkIkWgQjch0a6CJiQSEdHLi+GZiCoFuYUIr1W3xGvVLfVt/2SrcTnJMFCn5Zm0QBDuZKlx\nJ+sxdsXrJiQKAPzkEjR1kcFTK0FneR4aOkphKeFwDyIiMh3DMxFVWu7WYrzhZYU3vKwA6NaVj89U\n41KSLkhfSVLiWrIS2apnB2otgN/SVPgtTQVAhvl/JEIqAho4ShHorBvyEZC/wodUxEBNRERP99zh\n+fTp09i2bRv++ecf1K1bFyNHjkSNGjXKsjYiIgOCIKCWvQS17CV4y8cagG5C4m9pqvwwreul/jVF\nCRPyNJQa4FqyLoD/9/cnVvjID9OBLjL4OUggZqAmIiI8IzzPnTsXS5YswY0bN+Di4qJv37x5M8aO\nHQutVvfb6ciRI9i2bRuOHj2q3/2PiF4tgwcPNsvrSkQC/J2k8C8yIfGxSotfUpS4nJSHS/k91LHp\npk1INFzhQ8daIqCJsxQB+T3UgS5S1LbnknlERK8io+H59OnTaN++vUFwzs3NxdSpU2Fvb48NGzYg\nKCgIkZGRGD16NCIiIrB48eJyL5qIKp8lS5aYuwQ9K4mA5q4yNHeV6dvS8zS4mqQL1GfiU/B7rgXu\nZqlNul62SovzD/Jw/kEeii6Z1yR/ybzA/B7qmrZcMo+I6GVnNDzfvn0b//73vw3aTp48iczMTHz2\n2Wdo06YNAKBXr144ceIETpw4UW6FEhG9CAeZCG2rW6BtdQu8afUPfH1rIilHjav5y+VdSdZ9/tvE\nFT4ylVqc+ScPZ4osmSeXCQjM38wlwEWGQGcpPLgGNRHRS8VoeE5NTYW7u7tB2+nTpyEIAjp37mzQ\nHhAQgB9++KHsKyQiKiculmJ09BSjo2fhCh9/Z6txNT9MX80fQ52UY1qgTsvT4vj9XBy/X7hknsJS\nhMD8MN3URYpAZxncrLkGNRFRVWU0PLu5ueHvv/82aDt//jysra1Rr149g3aRSASZTAYioqqsmrUY\n1bys0LXICh/3HqlxJUmJq8m68dNXSrFkXmKOBpH3chFZZA3q6tai/DCtG/IR4MxNXYiIqgqj4Tko\nKAhbtmzB8OHDIZfL8csvv+DKlSvo0qULxGLDH/QxMTHw8PAo12KJiCqaIAioYStBDVsJengbLplX\ndLjHtWQlMpWmBer72Rrcv5OD/Xdy9G1etmLd2GlnXaCuJ5fC1UrEIR9ERJWM0fD88ccfo23btggK\nCoKfnx9u3LgBQRAwfvx4g/O0Wi327t2L9u3bl2uxRESVQdEl83r76No0Wi3i0lX6MH01fw3qx+rS\nbOqixu74wkBtLxVQx0GCOg4S+NpL8h9LUdteDGsJd0skIjIHo+HZz88PP/30ExYuXIj4+HgEBwdj\n3LhxaN68ucF5p0+fhq2tLXr06FGuxRJR5SWXyw2+TktLM1Ml5iESBNSVS1FXLkW/2oVrUMekqXAl\nOU8/MfFGihJ5pg2hRoZSq9tdsciyeQU8bcTwzQ/Wdewl+seeNmIuoUdEVI6euUlKixYtsG3bNqPn\ntGnTBufOnSuzooiIXgYSkYCGTlI0dJLiX766tjy1FjdTlbia30N9JUmJm6mmbepS1L1Hatx7pDaY\nnAgAVmIBPvbi/N5qqe5zfrB2kLG3mojoRb3Q9twajQbJyclwcXHhuDwiIhPIxAICXGQIcJFhiJ9u\nU5cclRa/pBaG6V9SlIjLUJm07fiTHqu1+DVVhV9TVQByDI4pLEX6MF04DEQCbzsJtyQnIjKR0fAc\nFxeHixcvomvXrgZ/ks3KysLkyZOxc+dOKJVKODo64tNPP8V7771X7gUTEb1sLCUCmilkaKYoXLFI\nq9XifrYGcem63RHjMlSIS1chNl2FO1lqlD5W61b+SMwp2OylkEQAvO0khb3U9oWPFZactEhEVJTR\n8LxixQocPnwY/fr1M2ifOHEitm/fDh8fH/j7+yM6OhqTJ09G9erV0bVr13ItmIjoVSAIAjxsxPCw\nEaNtdcNjOSotbmfqwnRchi5QF4RsU5fQK0qlhS6cZ6hw8K7hMXuZUNhLbS+Br4NuKIjWtM0ZiYhe\nOkbDc1RUFDp16gSRqHCc3N9//40dO3agWbNm2L9/P6RSKdLS0tCuXTt8++23DM9EROXMUiKggaMU\nDRylxY4l56gRm14QqAt7rG9nqqA0caJiURl5WlxKUuJSsUmL1rC5eB/OliIoLEVwsRTB2VIMl/yv\nnS1FcLEUQ2FV8FjEFUKI6KVgNDzfv38fvr6+Bm2RkZEAgJEjR0Iq1f3glsvl6NevH7799ttyKpOI\niEzhbCmGs6UYIW4WBu0qjRZ3stS6oR8ZhT3Vcekq/PP4OVI1gEcqLR7lL7FnChuJoA/SihLCtoul\nCC5WDNtEVHkZDc8qlQpWVlYGbefPnwcAhIWFGbR7enoiMzOzjMsjIqKyIBEJ8LGXwMdegk5PHMtU\navBHfm91bH5PdVy6Cn9kqPDoOSYtlqS0YdtaIujCtP5D/NSvnS1FUFgxbBNRxTAanmvWrImrV68a\ntJ05cwbVq1dHtWrVDNozMjLg5ORU9hUSEVG5spOK9CuAFFV00mLh2Grd578eqaDSlu9EwmyVVr95\njCms83u2C4aROFmI4Fjk48mv5TIR7GUC18UmolIxGp579uyJiIgIhISEICQkBFu3bsVff/2FcePG\nFTv34sWLqFWrVrkVSkREFcvYpMXff4+Fa83aSM7RIClHjcQcTf5jDRJz1EUea5Cco0ZSjua5xlyX\nRrZKi+wsNe6aGLYBQCwAcllBoBZ0obpo0JY9PYAzdBO9uoyG5zFjxmDfvn0YNWoUBEGAVqtF3bp1\nMWHCBIPzkpOTcfDgwWLtRET0chIEQJ4fNGs7PHvLAK1WiwylFkmPdWE7KT9cJ+WU/HV5h20AUGuB\n5FwNknNL92ICALmFAEeZCE6WhSFbXlJPt0wXzh1kIoi5pjZRlWb0J561tTWOHDmCvXv3Ij4+Hl5e\nXujWrRssLAwnovz999/49NNPER4eXq7FEhFR1SQIAhxkuvBYlcO2vj4AqblapBdSkIcAACAASURB\nVOaqcTvT9J5uAYCDTNCHaqnKAu73kuEgE8FequvRdpCJYC8TwUEm5H8WwV6qa7eTCgzfRGb2zJ9g\nEokEPXv2NHqOv78//P39y6woIiJ6tZVF2E7J1SAtV4PUPA1SczVIzdUiJbfgse5YVhlOiDSFFkBa\nnhZpeWr8makGIAbScp71NAN2+UHaXirAwaIwWBcN3PbSJ8K3PpQLsBIL3PiG6AUY/Ymk0WiwZMkS\nuLu749133y3xvC1btuDBgwcYP358mRdIRET0LKUN2wXy1FpdmM4rDNWGH08/nqms2NBdVKZSi0zl\n8+9SIxXBSC+3kB+8dcft83u7baUi2EoF2OV/tpWwB5xeXUZ/wmzduhWzZs3C0aNHjV6kfv36+OCD\nD1CtWrViuxES0auhSZMm5i6BqNRkYgFu1mK4WYtL9TylRqvr1c7/0Pdo52n1vdopTwbxPA0ynmMH\nyLKm1BSM8waA5w/h1hIhP1AXhmtbaX7Ylgiwk5nQlh/ILcQM4lR1GA3P27dvR8eOHREQEGD0IgEB\nAejcuTO2bNnC8Ez0ijp58qS5SyCqMFKRAIWVGAqr0oVulUaLtCK92Lfi78HWpRoy8rRIz9MgQ6kp\nfJynQXqetvCz0rw93k/KVmmRrdLi4WPgRUI4oOsN14dqSf5nmaBvs5XoQvaTbbZSEVIzRchLUcJa\nIsCq4EMsQCoCh6dQuTAanq9du4ZJkyaZdKHWrVtjwYIFZVIUERHRy0giEvI3d9GFbsd0DXx9rE1+\nvlqjRaZSF651YVuL9Fzd54yCtiJBvCB8F7Sl52mQV4ETK02l1BROwCw9S+Daw2KtYkHXO24p1gXq\npz0uCNxFH1uLBVg+8dg6P5AXfWxV5LlctvDVYjQ8Z2VlwcHBwaQL2dvbIysrq0yKIiIiouLEIgFy\nCwFyi+ffTTFHpc0P1kV7ufPbcjVIVxb2fGfkaZGl1E2szFLqHmfmaSt8ouXzUGsLxoeXf62WYuSH\nbZEuUOcH74LHthIBNlIBNpLCIS42EgE2UlF+m5DfJoJNkceWYvaeV0ZGw7OzszPi4+NNulBCQgKc\nnZ3LoiYiIiIqJ5YSAZYSMVxLOeSkKI1Wi0dPBOpMZdGgnR+ylVpkPqUtS6lBZpG2KpDFjcpRAzlq\nLVJfcPjKk0QC8oenFAZtG2lBGC8M3jb5w1hsioRy2yLnFYZ1rrZSFoyG5+DgYPz444+YMmUKpFJp\niecplUrs2LEDwcHBZV4gERERVS4iQTdR0E4KAM8fwgHdMoO5aiBLpckP21pk5mn0ITtLVRjMM/MM\n2zLzNEh99BhaiQUeq7R4rNbicf5YbHUVD+QAoNFCNyRHqQVQNuNtCgK5TZGebpHSAo63k2AhLhyK\nYikWYCmB/rGVWIBFwZCW/MeG5wqwFEM/NMYi/zmSl3BVFqPheeTIkejatSuGDRuGFStWwNbWttg5\njx49wpgxYxAfH4+VK1eWW6FERET08hGE/JAmEcPFsvTPj42Nha+vV7F2pUYXonPyQ3XB4+z8gF00\nbD8ucs5jlRY5RR4XnqPBYzV0n4u055RtZ3O5e3ogFwMZueXyehIBRcL1U4J2CUG8IHxbSnT/UBtU\n16Zc6nseRsNzSEgIPv30U8yePRunT5/Gm2++iQYNGsDW1hZZWVm4efMm9u3bh5SUFHz88ccICQmp\nqLqJqJJp27atwddcfYOIzEkqKlj7u3xfR6PVhe2CHm+D4J3fll0wxEWlwSOlbsjLo/yvs5Ta/DZN\nfpuud/2RUlspJ3eWlkoL3Xt6gbE5LpaiqhOeAWDy5Mnw8/PD7NmzsXHjxmLH69ati4iICG7NTfSK\nu3btmrlLICKqcCJBtwKHtQQo65lfeeqC4K0pMsa8MGg/yj+W9UQgL3qsIJAXBPTnWtDEzCwr2Trg\nJm3D1KNHD/To0QN//vknfvvtN2RmZsLOzg5+fn7w8fEp7xqJiIiIXjkysQCZ+MVWV3mSUpMfsvMD\n+SOlFr/H34VzNQ/kqHVDW3LU2uKP8ydFPlZpkavWDVvJVRcOczE8v/Dcshh6XiXDc4FatWqhVq1a\n5VULEREREZUj6VOWO7RL08DX8zkGnD+DVquFUgODoF0QvHNUhSH76WG9cLy6Uxn+46EsGA3PDRs2\nRGhoKIKDgxEaGgp/f/+KqouIiIiIqjBBECAT63rQXyZGw7OHhwf27NmDH3/8EYIgwM7ODi1atEBo\naChCQkIQFBQECwuLiqqViIiIiMisjIbnyMhI5Obm4tKlS4iKisKFCxcQFRWFI0eO6P41IZMhICAA\nISEh+g+5XF5RtRMRERERVahnjnm2sLBAWFgYwsLC9G2//vqrPkxfuHABS5cuxdKlSyESiZCUlFSu\nBRMRERERmUupJgwWaNiwIRo0aIBmzZohKCgI//vf/xAVFQWN5iVYkJCIiIiIqAQmh+ecnBxcvHhR\n39t88eJFZGVlwdHREc2bN8eMGTO4PTcRERERvdSMhue9e/fqw/K1a9egVqvh6+uLFi1aYPbs2QgO\nDoavr29F1UpEREREZFZGw/PAgQMhlUrRq1cvTJkyBc2bN4ejo2NF1UZEREREVKkYXXU6JCQEYrEY\n27Ztw0cffYSPP/4Y3333HX799VdotWWxZ0zVs3btWjRu3Bhubm5o27Ytzp07Z+6SiIiIiKiCGO15\nPnDgAJRKJa5cuYKoqCicP38es2fPRnJyMuzs7NC8eXOEhIQgODgYzZo1g7W1dUXVbRY7d+7EJ598\ngkWLFiEkJARr165F3759ceHCBdSoUcPc5RERERFROXvmfodSqRQtWrTA2LFj8f333yMuLg4XLlzA\nrFmz4Obmhi1btqBnz56oWbMm2rdvXxE1m82KFSvQv39/DB48GH5+fliwYAHc3Nzw3Xffmbs0IiIi\nIqoAQlpa2nONv9BoNLh27RrOnTuHn376CdHR0RAEASkpKWVdY6WQl5eHatWqYd26dejZs6e+fdKk\nSbh58yb279//1OfFxsZWVIlERERE9IKetRiGyUvVPXr0CBcvXsT58+dx4cIFXLp0CdnZ2dBqtbC2\ntkbr1q0REhLywgVXVsnJyVCr1VAoFAbtCoUCDx8+LPF5XI2kUGxsLO/HC+I9LBu8jy+O97Bs8D6+\nON7DF8d7WDpGw/Pu3bv1YfnXX3+FWq2GVquFQqFAu3btEBISgtDQUDRp0gRisbiiaiYiIiIiMguj\n4XnIkCEAgNq1a6Nfv376sFy7du2KqK1ScXZ2hlgsRmJiokF7YmIiXF1dzVQVEREREVUko+F5w4YN\nCA0NhYuLS0XVU2nJZDIEBATg+PHjBmOejx8/jh49epixMiIiIiKqKEbDc/fu3SuqjiphzJgxGDFi\nBIKCghAcHIzvvvsO//zzD4YOHWru0oiIiIioApg8YZCA3r17IyUlBQsWLMCDBw9Qv359bNu2DV5e\nXuYujYiIiIgqAMNzKQ0bNgzDhg0zdxlEREREZAbP3CSFiIiIiIh0GJ6JiIiIiEzE8ExEREREZCKG\nZyIiIiIiEzE8ExERERGZiOGZiIiIiMhEDM9ERERERCYS0tLStOYugoiIiIioKmDPMxERERGRiRie\niYiIiIhMxPBMRERERGQihmciIiIiIhMxPBMRERERmYjhmcpFSkoKNmzYgAEDBiAwMBDu7u7w8vJC\nly5dsGHDBmg0GnOXWGX98MMPkMvlkMvl2LBhg7nLqVJOnjyJAQMGoG7dunB1dUW9evXQu3dvREZG\nmru0KuHQoUPo1asXGjRoAHd3dzRp0gSDBw9GdHS0uUurVHbv3o3Jkyeja9euqFGjBuRyOYYPH270\nOVFRUejbty+8vb3h7u6OsLAwrFy5Emq1uoKqrlxKcw//+OMPLF68GN27d0fDhg2hUCjg6+uLd999\nF6dOnargyiuX5/leLGrs2LH63ze3b98ux0qrFom5C6CX065duzBx4kS4u7ujdevW8PT0xMOHD7Fn\nzx6MGzcOR44cwfr16yEIgrlLrVLu3buHyZMnw9bWFllZWeYup0qZPn06li5dCg8PD3Tt2hXOzs5I\nSkrC1atXcebMGXTq1MncJVZqM2bMwJIlS+Dk5IRu3brB2dkZt2/fxv79+/HTTz9h9erV6Nevn7nL\nrBQWLFiAX375Bba2tqhevToyMzONnr9v3z4MGjQIlpaW6NWrFxwdHXHw4EF8+umniIqKwvr16yuo\n8sqjNPfwq6++ws6dO1GvXj28/vrrcHR0RGxsLA4cOIADBw5g7ty5GDlyZAVWX3mU9nuxqAMHDmDj\nxo38ffMUXOeZysXJkyeRnZ2Nzp07QyQq/APHgwcP0KFDB9y7dw/r169HeHi4GausWrRaLXr27ImE\nhAR0794dy5Ytw9KlSzFo0CBzl1bprV+/Hh9++CHeffddLFmyBDKZzOC4UqmEVCo1U3WV34MHD1C/\nfn24uLjg7NmzUCgU+mOnTp1Cjx49ULNmTVy7ds2MVVYep06dgoeHB3x8fHDmzBl0794db7/9Nr75\n5pti52ZkZKBp06bIyMjAoUOHEBgYCADIyclBjx49EB0djXXr1qFPnz4V/TbMqjT3cPPmzfD390eT\nJk0M2s+cOYNevXpBEARcv34d7u7uFVV+pVGa+1hUUlISwsLC0KpVKzx48ABnz57F5cuX4ePjU0GV\nV24ctkHlom3btujatatBcAYANzc3DB06FIDuBxuZbvXq1Th16hRWrFgBa2trc5dTZeTm5uLLL7+E\np6fnU4MzAAbnZ7h79y40Gg2CgoIMgjMAtGnTBnZ2dkhOTjZTdZVPmzZtULt2bZP+srZ7924kJSWh\nd+/e+uAMAJaWlpg2bRoAYN26deVWa2VVmns4YMCAYsEZAFq1aoVWrVohLy8PUVFR5VFmpVea+1jU\nhx9+CABYuHBheZRV5XHYBlW4gqAikfDbz1QxMTH4/PPPMXLkSLRs2fKVH8dXGsePH0dSUhJGjRoF\nkUiEQ4cO4datW7CwsEBQUBBatGhh7hIrvdq1a0Mmk+Hy5ctITk6Gs7Oz/tjZs2eRmZmJbt26mbHC\nquv06dMAgI4dOxY71rJlS1hbWyM6Ohq5ubmwsLCo6PKqPP6+Kb3Nmzdj37592Lx5M5ycnMxdTqXE\n7yaqUCqVClu3bgXw9F8WVJxKpcKIESPg6emJ6dOnm7ucKufy5csAdD15bdq0wc2bNw2Oh4WFYcOG\nDXBxcTFHeVWCo6MjZs6ciWnTpiE4OBjdunWDk5MT/vzzTxw4cADt2rXD4sWLzV1mlRQbGwsAqFOn\nTrFjEokENWvWxK1btxAfHw8/P7+KLq9Ku3PnDk6ePAlra2u0bNnS3OVUCXfu3MHUqVPx9ttv8x/E\nRjA8U4WaOXMmbt68iU6dOqFDhw7mLqdKmDdvHq5fv46DBw/CysrK3OVUOUlJSQCApUuXws/PDwcO\nHECjRo2QkJCAzz77DMeOHcPgwYOxb98+M1dauY0ePRpeXl744IMPDCaw+fj4oH///sWGc5BpMjIy\nAAD29vZPPV7Qnp6eXmE1vQxyc3MxfPhw5Obm4osvvoBcLjd3SZWeRqPBqFGjYGNjg/nz55u7nEqN\nY56pwqxevRrLly9H3bp1sWbNGnOXUyX8/PPPiIiIwAcffMDhBc+pYFlEiUSCLVu2IDQ0FLa2tmjY\nsCE2bdoEDw8PnD17lsutPcOSJUswePBg9O/fH1evXsX9+/dx4sQJeHt74/333+dfRajSUKvVGDFi\nBC5cuIDevXtj7Nix5i6pSlixYgXOnj2LJUuW8B8bz8DwTBXim2++wSeffIJ69ephz549cHR0NHdJ\nlZ5KpcLIkSNRp04d/cQhKj0HBwcAQOPGjVGzZk2DY9bW1mjfvj0A4NKlSxVeW1Vx+vRpzJgxA127\ndsXs2bPh7e0Na2trBAQEYNOmTahevTqWL1+O+Ph4c5da5RT0LBf0QD+poL3g+5iMU6vVGD58OHbt\n2oVevXrhm2++4ZKoJoiLi8OsWbMwYMAALttpAoZnKncrV67ElClT0KBBA+zZswdubm7mLqlKyMrK\nQlxcHGJiYuDm5qZfqF4ul2PevHkAgHHjxkEul+OTTz4xc7WVV8FY0pLCR0EPS05OToXVVNUcOnQI\nANC6detix6ytrdG0aVNoNBouVfccfH19AejCy5NUKhUSEhIgkUjg7e1dwZVVPUqlEu+99x5+/PFH\n9O3bF2vXruVEQRP99ttvyM3NxebNmw1+18jlcpw9exYA0LRpU8jlcuzdu9fM1Zofv6uoXC1evBgz\nZ85Eo0aNsGvXLoNZ+mSchYUFBg4c+NRj165dw/Xr1xEaGoo6depwSIcRbdu2hSAI+O2336DRaIot\nn3jr1i0AKNYrTYVyc3MBFI4ff1LBMnVPWwaQjGvdujW2bduGI0eO4K233jI4dvbsWWRnZyMsLIwr\nbTxDXl4ehgwZgv379+Odd97BypUri/2/TiXz8vIq8fdNZGQkHjx4gJ49e8LOzg5eXl4VXF3lw/BM\n5Wb+/PmYPXs2AgIC8L///Y9DNUrJysoKy5Yte+qxOXPm4Pr163j33Xe5ScozFGwLf+DAAaxatQpj\nxozRHzt27BiOHj0KBwcHTmA1IiwsDN9++y3Wr1+PoUOHonr16vpjhw8fxoULF2BpaYng4GAzVlk1\nhYeHY+bMmdi5cydGjBhhsEnKV199BQB47733zFlipZebm4uBAwciMjISAwcOxJIlSxicS6lx48Yl\n/r7p1q0bHjx4gOnTp3OTlHwMz1Quvv/+e8yePRtisRihoaFYvXp1sXO8vLwwYMAAM1RHr5qFCxfi\nxo0bmDZtGiIjI9G4cWMkJCRg3759EIvFWLp0KceUGhEeHo7XXnsNJ06c0C9V5+bmhpiYGBw6dAha\nrRYzZszgmrD59u7dq1+95eHDhwCA6OhojBo1CgDg7OyMWbNmAdCNeS6YjPnmm2+id+/ecHR0xIED\nBxAbG4vw8HD07t3bPG/EjEpzDydMmIDIyEg4OzujWrVq+mFtRbVq1eqpw45edqW5j2Q6hmcqFwkJ\nCQB0kzdWrVr11HNatmzJ8EwVwsPDAydOnMC8efNw4MABnDt3DnZ2dujSpQsmTpyIoKAgc5dYqYlE\nImzfvh3ffvstdu7ciX379iE7OxuOjo7o1KkTRowYoZ94ScCNGzewZcsWg7b4+Hj9hMoaNWoYBJY3\n33wT+/btw6JFi/DTTz8hNzcXPj4++OqrrzBy5MhXcsJbae5hwe+b5ORko0usvYrhubTfi2QaIS0t\nTWvuIoiIiIiIqgIOCiIiIiIiMhHDMxERERGRiRieiYiIiIhMxPBMRERERGQihmciIiIiIhMxPBMR\nERERmYjhmYiIiIjIRAzPRESV0OnTpyGXy/Hjjz+auxSTrVq1CgEBAXByckKrVq1e6FqbN2+GXC7X\nb4BBRFRZMDwT0SurIKC5urri7t27xY7369cPjRo1MkNlVc/58+cxdepUBAUFYfny5Zg+fbq5SzIq\nKioKc+bMQVpamrlLIaIqhuGZiF55eXl5iIiIMHcZVdqZM2cAABEREejfvz86depk5oqMi46Oxrx5\n85Cenm7uUoioimF4JqJXXqNGjbB58+an9j6/7B49elQm10lMTAQAODg4lMn1qqqyup9EVHkxPBPR\nK2/ixIkAgEWLFhk9LyEhAXK5HJs3by52TC6XY86cOfqv58yZA7lcjpiYGAwfPhxeXl7w8fHBF198\nAa1Wi/v376N///6oUaMGfH19sXTp0qe+plqtxuzZs1GvXj1Uq1YNvXv3xh9//FHsvLi4OAwZMgS1\natWCm5sbWrdujd27dxucUzBM5eTJk5gyZQp8fX3h4eFh9D2r1WosXLgQgYGBcHV1hb+/P6ZPn47H\njx8bvPdvvvlG/7ike/Rkve+99x7q1KkDNzc3NG3aFJ988onR5zRq1AijRo0q1t6tWzd069bNoG3t\n2rUICwtD9erV4eXlhVatWuE///kPAN1/m88++wwA0KRJE33Np0+f1j//2LFjeOONN+Dh4QEPDw/0\n6dMH169fN3iNUaNGwc3NDQkJCXjnnXdQo0YNvP322wCAhw8fYuzYsWjYsCFcXV3h6+uLt956C7du\n3TL6Homo8pOYuwAiInPz9PTEv/71L2zcuBEfffQRatSoUWbXfu+991C3bl3MmDEDkZGRiIiIgKOj\nIzZt2oSwsDDMnDkT27dvx/Tp09GkSRO0bdvW4PmLFy+GRqPBBx98gLS0NKxZswbdu3fH2bNn4ejo\nCACIiYlBp06d4Obmhg8//BA2NjbYu3cvBg8ejDVr1qBfv34G1/z4448hl8vx0UcfISMjw2j948eP\nx8aNG9G9e3eMGTMGV65cwdKlS3Hr1i1s27YNgiBgzZo12Lp1K44fP441a9YAAIKDg0u85q1bt9C5\nc2eIRCIMGTIE3t7euHPnDnbu3Im5c+c+z202sGHDBkyaNAnh4eF4//33oVQq8dtvvyEqKgpDhw5F\n9+7d8ccff2DHjh2YPXs2nJ2dAQB+fn4AgO3bt2P48OFo164dpk+fjry8PPz3v//FG2+8gWPHjqFu\n3br619JoNOjduzeCgoLwxRdfQCwWAwAGDx6MX3/9Vf8Pp+TkZJw9exZxcXGoX7/+C79HIjIfhmci\nIuh6nzdt2oRFixZh8eLFZXbdgIAALF++HAAwZMgQNG7cGNOnT8e0adMwadIkAECfPn1Qv359bN68\nuVh4TkxMxMWLFyGXywEArVu3Rnh4OFasWIH/+7//AwB88sknqFatGo4fPw4rKysAwPvvv49evXrh\n888/x9tvvw1BEPTXLAjXEonxXwG//PILNm7ciP79+2PlypX6dk9PT8ybNw+HDh1Cly5d0K9fP/z8\n8884fvx4saD+NJMmTYJarcapU6fg7e2tby/oDX5Rhw4dQv369bF+/fqnHvf390eTJk2wY8cOdOvW\nDTVr1tQfe/ToESZPnoz+/ftjxYoV+vaBAweiWbNmmD9/PtauXatvVyqV6Ny5M2bPnq1vS0tLw/nz\n5/Hll19i7Nix+vYJEyaUyfsjIvPisA0iIhT2Pm/evBl37twps+sOGjRI/1gsFiMgIABarRYDBw7U\nt8vlctSpUwfx8fHFnv/OO+/ogzMAtG3bFvXr18fBgwcBAKmpqThx4gR69uyJ7OxsJCcn6z86dOiA\n+/fvIy4uzuCagwcPfmZwBoDIyEgAwJgxYwzaR48eDbFYrD9eGklJSTh79iz69+9vEJwBGAT8F2Fv\nb4+//voLly9fLvVzjx8/jrS0NPTt29fgXqrVaoSGhhoM7SgwbNgwg6+trKwgk8lw5swZpKamPvf7\nIKLKieGZiCjfxIkTIQjCM8c+l4anp6fB1/b29pBKpXBzcyvW/rRl02rXrv3UtoKAf/v2bWi1Wsyd\nOxe1a9c2+CjomS6YzFfgydBakrt370IQBNSpU8eg3cHBAe7u7s/1j4yCfyCU59CF8ePHw87ODu3b\nt0dAQAAmTJiAU6dOmfTcgvHkPXv2LHY/9+zZU+xeikQieHl5GbRZWFhg5syZOHLkCHx9fdGlSxcs\nWrQI9+7dK5s3SERmxWEbRET5PD09MXDgQGzYsAEfffRRseMl9Yyq1eoSr1kwBrYokejp/RZardbE\nSgtpNBoAut7gkpaHa9CggcHXBUM7qpqS7r9GozG4p35+frh48SIOHz6Mo0eP4tChQ/jPf/6DYcOG\nYeHChUZfo+B+rly5EtWrV39mTVKp9Km9+KNHj8Ybb7yB/fv348SJE1iwYAEiIiKwdetWtG7d+pnX\nJaLKi+GZiKiIiRMnYuPGjU8NWQXDJ55cG7g8l7h72soaf/zxh763s6AXWSKR4LXXXivT165Rowa0\nWi3i4uLQsGFDfXtGRgb++ecfdO7cudTXrFWrFgA816oTcrn8qesy371712DcMgBYW1sjPDwc4eHh\nUKlUGD16NNauXYuJEycaDcUF9bm4uLzw/fT29sbo0aMxevRo/PXXX2jdujUWLVrE8ExUxXHYBhFR\nER4eHhg0aBC2bNlSLBTb29vD2dkZ586dM2gvOoGsrG3dutVgOMfJkyf1q1UAgEKhQOvWrbF+/Xrc\nv3+/2POTkpKe+7ULerJXrVpl0L569Wqo1ernCs/Ozs5o2bIlvv/++2JjvJ/V816rVi38/PPPyMvL\n07cdPHiw2HCIlJQUg68lEom+970gfNvY2ABAsaEy7du3h4ODAyIiIgxep4Ap9zM7O9tgKT9A932l\nUCi4KQvRS4A9z0RET5gwYQI2btyImzdvFlu2btCgQfj6668xduxYBAYG4ty5c8Um5JUlhUKBLl26\n4F//+hfS09OxevVquLu7G0zii4iIQOfOndGyZUsMHjwYtWrVQmJiIn7++WfExMTgypUrz/Xa/v7+\nGDhwIDZu3IiMjAy0adMG165dw6ZNm9CxY8fn3kVw/vz56Nq1K1577TUMHToU3t7euHv3Lnbu3Gl0\nkt+gQYOwe/du9OnTB7169cKff/6Jbdu26XuLC/Tq1QsKhQIhISFwdXXFn3/+iW+++QYNGzbUL0cX\nGBgIAPjiiy/w1ltvQSaToU2bNlAoFPj666/x/vvvo02bNujTp49++/ajR4+iXr16xf4x8aS4uDj0\n6NEDPXv2RL169WBhYYHIyEjExMTgyy+/fK57RkSVB8MzEdETCnqfv/3222LHpkyZgqSkJOzevRu7\ndu1Cx44dsWPHjmKT6srK+PHjERsbi2XLliE9PR2hoaGYP38+nJyc9Of4+vri+PHjmDdvHrZu3Yrk\n5GS4uLjA398f06ZNe6HXX7x4MWrWrIlNmzbhwIEDcHV1xdixYzF16tTnXh2jYcOGOHz4ML766iv8\n5z//QU5ODjw8PNClSxejz+vQoQNmzZqFlStXYurUqQgMDMQPP/xQ7D0OHToU27dvx6pVq5CZmQl3\nd3cMGDAAkydP1o+NDgwMxIwZM7Bu3TqMGTMGGo0Ge/bsgUKhQO/eveHup0ioVgAAAKFJREFU7o6I\niAgsX74cubm5cHd3R3BwMIYOHfrM9+fp6Ym+ffvi1KlT2LFjBwRBQO3atbFs2TKDVVaIqGoS0tLS\nSj9DhYiIiIjoFcQxz0REREREJmJ4JiIiIiIyEcMzEREREZGJGJ6JiIiIiEzE8ExEREREZCKGZyIi\nIiIiEzE8ExERERGZiOGZiIiIiMhEDM9ERERERCZieCYiIiIiMtH/Ax06iznHrcXeAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22450ceb358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wcss = []\n",
    "for i in range(1, 16):\n",
    "    kmeans = KMeans(n_clusters = i, init = 'k-means++')\n",
    "    kmeans.fit(X)\n",
    "    wcss.append(kmeans.inertia_)\n",
    "\n",
    "with plt.style.context(('fivethirtyeight')):\n",
    "    plt.figure(figsize=(10,6))\n",
    "    plt.plot(range(1, 16), wcss)\n",
    "    plt.title('The Elbow Method with k-means++\\n',fontsize=25)\n",
    "    plt.xlabel('Number of clusters')\n",
    "    plt.xticks(fontsize=20)\n",
    "    plt.ylabel('WCSS (within-cluster sums of squares)')\n",
    "    plt.vlines(x=5,ymin=0,ymax=250000,linestyles='--')\n",
    "    plt.text(x=5.5,y=110000,s='5 clusters seem optimal choice \\nfrom the elbow position',\n",
    "             fontsize=25,fontdict={'family':'Times New Roman'})\n",
    "    plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
